The key to all of this is that people are reporting that their streaming music, i.e. from iTunes radio stations, are also manifesting the same problem. It's easy to test. So it's not just music that was not purchased from them.
The fact that music NOT purchased from the iTunes store won't play is almost immaterial given that internet radio stations are also a problem.
If AAC format is playing but standard MP3s are not, as well as the internet radio stations, there may also be a codec issue? Y/N?
As noted I went back to iTunes 10.4. There is an archive copy at FileHippo.Com. If you downgrade you need to remove the existing 10.5, and also delete the iTunes library (.itl) file. You will loose your library contents but it is necessary as the 10.5 library will not talk to the 10.4 iTunes. The library will be re-created when you launch 10.4 and you will have to re-populate it. There is no such thing as a free lunch it seems.
I also loaded Tapin Radio for streaming for now. Actually not bad.